by using a solder sucker, man! there is a tool that is basically a little bulb with a tube on it...kinda like a baby booger getter...no kiddin'. just put your iron on the solder you want to remove and use the solder removal tool to get off the excess. it's not necessary to solder the ground wire to the bridge. as long as it's touching, you should be good. solder isn't going to enhance the connection between the two.

you can also purchase a solder removing ribbon and that will of course remove solder.you use it by putting the Romover ribbon on top of the solder and pressing the Soldering Gun/Iron against the ribon (which will sandwich the ribbon in between).Do not let solder cool when ribon in sandwiched because it will stick.

I would solder the wire to the bridge (if you can some metals wont solder). Simply because we get so many questions saying "I get this tingling feeling from my strings.. oh yeah the earth wire fell off".